New Trends and Applications of Differential Geometry
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".
Deadline for manuscript submissions: 30 November 2026 | Viewed by 500
Editors
Interests: geometry
Special Issue Information
Dear Colleagues,
Differential geometry is a foundational branch of mathematics that investigates how the geometric properties of curves and surfaces evolve point by point, providing a rigorous framework for studying complex structures in space. Historically, the evolution of this discipline has been inextricably linked to the development of analytic geometry, particularly through the pioneering 17th- and 18th-century studies of curves and surfaces.
The classical study of Special Curves on Surfaces incorporating fundamental structures such as Evolute–Involute Curve pairs has long provided a rich basis for understanding the interplay between curvature and torsion. These curves are not merely geometric constructs; they represent the fundamental language through which we describe the local and global behavior of manifolds. In recent years, this field has undergone a significant transformation, expanding into more generalized frameworks such as the intricate study of Rectifying Curves and the geometric characterization of Slant Helices Curves.
Today, the power of modern analysis has propelled these classical concepts into diverse and specialized domains. The investigation of Quaternionic and Magnetic Curves has bridged the gap between pure geometry and physical applications, offering new insights into motion in force fields and high-dimensional space representation. Simultaneously, the integration of Kinematic Geometry remains a vital area of research, providing elegant solutions to complex problems involving motion and transformation in both Euclidean and non-Euclidean geometries.
Furthermore, the Approximation of Surfaces Along Curves has emerged as a crucial technique in contemporary geometry, facilitating a deeper understanding of the local geometry of developable and Ruled Surfaces. These advances are closely related to the structural analysis of singularities, caustics, and the broader topological invariants of manifolds.
The purpose of this Special Issue is to report recent theoretical advances and innovative applications within these research fields. We are seeking contributions of original research papers that explore the geometry of special curves, surface approximations, and their multidisciplinary implications in the modern mathematical landscape.
Prof. Dr. Yusuf Yaylı
Dr. Zehra Özdemir
Guest Editors
Manuscript Submission Information
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Keywords
- special curves on surfaces
- evolute-involute curves
- approximations of surfaces along curves
- quaternionic curves
- magnetic curves
- rectifying curves
- slant helices curves
- ruled surfaces
- kinematic geometry
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